Buckdahn, Rainer; Ma, Jin Stochastic viscosity solutions for nonlinear stochastic partial differential equations. II. (English) Zbl 1053.60066 Stochastic Processes Appl. 93, No. 2, 205-228 (2001). In Part I of this paper [see above, Zbl 1053.60063)] stochastic viscosity solutions to nonlinear stochastic partial differential equations were introduced and sufficient conditions for them to exist were found. In Part II, it is shown that under the same hypotheses uniqueness for stochastic viscosity solutions holds as well. Reviewer: Jan Seidler (Praha) Cited in 1 ReviewCited in 39 Documents MSC: 60H15 Stochastic partial differential equations (aspects of stochastic analysis) Keywords:stochastic partial differential equations; viscosity solutions; uniqueness Citations:Zbl 1053.60063 PDFBibTeX XMLCite \textit{R. Buckdahn} and \textit{J. Ma}, Stochastic Processes Appl. 93, No. 2, 205--228 (2001; Zbl 1053.60066) Full Text: DOI References: [1] Bertsekas, D. P.; Shreve, S. E., Stochastic Optimal Control, the Discrete Time Case. (1978), Academic Press: Academic Press New York · Zbl 0471.93002 [2] Buckdahn, R.; Ma, J., Stochastic viscosity solutions for nonlinear stochastic PDEs (Part I), Stochastic Process. Appl., 93, 181-204 (2001) · Zbl 1053.60065 [3] Crandall, M. G.; Ishii, H.; Lions, P. L., User’s guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. (NS), 27, 1-67 (1992) · Zbl 0755.35015 [4] Dellacherie, C.; Meyer, P., Probabilities and Potential. (1978), North-Holland: North-Holland Amsterdam · Zbl 0494.60001 [5] Lions, P-L.; Souganidis, P. E., Fully nonlinear stochastic partial differential equations, C.R. Acad. Sci. Paris Sér. 1, 326, 1085-1092 (1998) · Zbl 1002.60552 [6] Lions, P-L.; Souganidis, P. E., Fully nonlinear stochastic partial differential equations: non-smooth equations and applications, C.R. Acad. Sci. Paris Sér. 1, 327, 735-741 (1998) · Zbl 0924.35203 [7] Pardoux, E., Peng, S., 1992. Backward Stochastic Differential Equations and Quasilinear Parabolic Partial Differential Equations, Lecture Notes in Computers and Information Science, Vol. 176, Springer, Berlin, pp. 200-217.; Pardoux, E., Peng, S., 1992. Backward Stochastic Differential Equations and Quasilinear Parabolic Partial Differential Equations, Lecture Notes in Computers and Information Science, Vol. 176, Springer, Berlin, pp. 200-217. · Zbl 0766.60079 [8] Pardoux, E.; Peng, S., Backward doubly stochastic differential equations and systems of quasilinear SPDEs, Probab. Theory Related Fields, 98, 209-227 (1994) · Zbl 0792.60050 [9] Protter, P., Stochastic Integration and Differential equations, A New Approach. (1990), Springer: Springer Berlin · Zbl 0694.60047 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.